Question

Of all the Sunny Club members in a particular city, 25% prefer swimming on weekends and 75% prefer swimming on weekdays. It is found that 20% of the members in that city prefer swimming on weekends and are female, while 55% of the members in that city prefer swimming on weekdays and are female.
The probability that a club member picked randomly is female, given that the person prefers swimming on weekends, is_____.
P = Desired outcomes divided by the total outcomesm me

Answer 1

Answer:

The probability that a club member picked randomly is female, given that the person prefers swimming on weekends, is 0.8 = 80%.

Step-by-step explanation:

We use the conditional probability formula to solve this question. It is

$P(B|A) = \frac{P(A \cap B)}{P(A)}$

In which

P(B|A) is the probability of event B happening, given that A happened.

$P(A \cap B)$ is the probability of both A and B happening.

P(A) is the probability of A happening.

In this question:

Event A: Prefers swimming on weekends.

Event B: Being female.

25% prefer swimming on weekends

This means that $P(A) = 0.25$

It is found that 20% of the members in that city prefer swimming on weekends and are female

This means that $P(A \cap B) = 0.2$

So

$P(B|A) = \frac{P(A \cap B)}{P(A)} = \frac{0.2}{0.25} = 0.8$

The probability that a club member picked randomly is female, given that the person prefers swimming on weekends, is 0.8 = 80%.